Abstract
One of the most uncertain parameters in stepped spillway design is the length (from the crest) of boundary layer development. The normal velocity profiles responding to the steps as bed roughness are investigated in the developing non-aerated flow region. A detailed analysis of the logarithmic vertical velocity profiles on stepped spillways is conducted through experimental data to verify the computational code and numerical experiments to expand the data available. To determine development length, the hydraulic roughness and displacement thickness, along with the shear velocity, are needed. This includes determining displacement height d and surface roughness length z0 and the relationship of d and z0 to the step geometry. The results show that the hydraulic roughness height ks is the primary factor on which d and z0 depend. In different step height, step width, discharge and intake Froude number, the relations d/ks = 0.22–0.27, z0/ks = 0.06–0.1 and d/z0 = 2.2–4 result in a good estimate. Using the computational code and numerical experiments, air inception will occur over stepped spillway flow as long as the Bauer-defined boundary layer thickness is between 0.72 and 0.79.
Highlights
Stepped spillways have gained interest for discharging excess flood water because of substantial energy dissipation along the chute due to the roughness of the steps
The objective is to first, calculate d and z0 from given velocity profiles in the developing turbulent boundary layer on stepped spillway and second, to establish a relationship between d and z0 with the variables describing the geometry and layout of a stepped surface, which may be more helpful to estimate the bottom shear stress and friction factor in practical applications, and third, to propose a new method to predict the distance from the crest to the air inception point over spillway flow, which may be more applicable for prediction of the inception point on stepped spillways of different slopes
In order to determine the boundary layer development length on skimming flow over stepped spillway, this paper adopted the first method described by Meireles et al [1] to estimate the location of the inception point, i.e., visual observation of the cross section where there is a continuous presence of air within the flow at the sidewalls or within the step cavities
Summary
Stepped spillways have gained interest for discharging excess flood water because of substantial energy dissipation along the chute due to the roughness of the steps. The objective is to first, calculate d and z0 from given velocity profiles in the developing turbulent boundary layer on stepped spillway and second, to establish a relationship between d and z0 with the variables describing the geometry and layout of a stepped surface, which may be more helpful to estimate the bottom shear stress and friction factor in practical applications, and third, to propose a new method to predict the distance from the crest to the air inception point over spillway flow, which may be more applicable for prediction of the inception point on stepped spillways of different slopes. In order to determine the boundary layer development length on skimming flow over stepped spillway, this paper adopted the first method described by Meireles et al [1] to estimate the location of the inception point, i.e., visual observation of the cross section where there is a continuous presence of air within the flow at the sidewalls or within the step cavities
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